Event Type:

Analysis Seminar

Date/Time:

Monday, October 15, 2012 - 05:00

Location:

Kidder 356

Local Speaker:

Abstract:

We discuss the standard plate equations (Kirchoff, Euler-Bernoulli, von

Karman) which arise in modeling the oscillations of thin membranes. The

dynamics of these models are highly dependent upon the nature of the

nonlinearity (nonlocal, cubic-type) and on the physical parameter which

corresponds to the thickness of the plate (and is regularizing for the

dynamics). The models under consideration are important in the mathematical

study of wing and panel flutter, when the plate is coupled to a flow

equation.

In the first talk, we discuss the model in full generality and introduce the

abstract setup needed for the semigroup approach. We then restrict to a

specific case (linear plate equation with nonlinear interior damping).

Well-posedness of this model will be demonstrated. In the sequel, we discuss

the well-posedness of the fully nonlinear model in the presence of the von

Karman nonlinearity (non-compact). Time permitting, the discussion will

include a dynamical systems approach to long-time behavior of solutions,

including stability estimates from multiplier methods. As the nonlinear

model has non-trivial stationary solutions, we will show the existence of a

compact, finite-dimensional global attractor in the state space.